Dynamic classification of escape time Sierpiński curve Julia sets

• Autorzy: Robert L. Devaney , Kevin M. Pilgrim
• Języki publikacji: EN

Abstrakty

EN

For n ≥ 2, the family of rational maps $F_{λ}(z) = zⁿ + λ/zⁿ$ contains a countably infinite set of parameter values for which all critical orbits eventually land after some number κ of iterations on the point at infinity. The Julia sets of such maps are Sierpiński curves if κ ≥ 3. We show that two such maps are topologically conjugate on their Julia sets if and only if they are Möbius or anti-Möbius conjugate, and we give a precise count of the number of topological conjugacy classes as a function of n and κ.

Kategorie tematyczne

• 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 202
• Numer: 2
• Strony: 181-198

Daty

wydano

2009

Twórcy

autor

Robert L. Devaney

• Department of Mathematics, Boston University, Boston, MA 02215, U.S.A.

autor

Kevin M. Pilgrim

• Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.

Identyfikatory

DOI

10.4064/fm202-2-5